Lawyers for former House speaker Salvatore F. DiMasi and a lobbyist who were found guilty of political corruption in 2011 will ask a federal appeals court Tuesday to overturn the convictions, in a case that could help to redefine the standards for political bribery in federal courts across the country.

Lawyers for DiMasi and his good friend, lobbyist Richard McDonough, will argue that a 2010 Supreme Court decision redefining what constitutes bribery should apply to their case and that they should be ­acquitted under the new standard.

DiMasi’s case, in spring 2011, was one of the first to go to trial following the Supreme Court decision known as ­Skilling v. United States, and lawyers and even the judge who oversaw DiMasi’s trial agreed that they were exploring new legal ground following the precedent-­setting decision.

The Supreme Court had essen­tially narrowed the scope of evidence that would constitute a federal crime of bribery by requiring that prosecutors prove there was an agreement to have a public figure take an official action for his benefit. A mere failure to disclose a conflict of interest, while working with a lobbyist, for instance, could not constitute bribery.

At the time of DiMasi’s trial, US District Court Judge Mark L. Wolf agreed with prosecutors that DiMasi and McDonough’s case would still apply under the new, redefined standard, allowing a jury to convict them of a bribery charge known as honest services fraud. Wolf ruled prosecutors did not need to prove a handshake or written agreement had taken place, as DiMasi’s lawyers had argued, but that a general understanding that DiMasi would take ­action in a way that would benefit him would constitute bribery.

But lawyers for DiMasi and McDonough argue that the case is yet to be properly tested by the US Court of Appeals for the First Circuit in Boston.

“This appeal raises important and novel issues that will help define the circumstances under which a United States attorney can bring prosecutions against state legislators and lobbyists,” said Martin ­Weinberg, who is representing McDonough before the Appeals Court. Weinberg also represented a defendant who had been acquitted at the trial and has conducted much of the legal ­review of the Skilling standard.

Thomas Kiley, DiMasi’s lawyer, would say only that the ­appeal is based in large part on the new Skilling ruling, and he referred to documents he filed.

“In this case, the District Court’s failure to give Skilling its appropriate force infected virtually every aspect of the trial, requiring reversal,” he said.

Federal prosecutors have maintained in lengthy court filings that DiMasi and ­McDonough’s convictions fall under the new standard, arguing that “Skilling did not alter the requirements for proving honest services bribery.”

Legal observers agreed that the Skilling standard has yet to be fully tested, but said that ­appellate courts have increasingly found that cases involving lobbyists who claim to be doing their jobs can still be applied under the new bribery standard when a general understanding of a conspiracy is involved. They also noted that at the time of the trial, Wolf rejected many of the arguments being made in the DiMasi appeal.

Also, prosecutors pointed out in court filings this week that an appeals court in Washington, D.C., recently held in a similar case that a lobbyist could be convicted under the new standard.

One of the judges sitting on the Appeals Court panel Tuesday is retired US Supreme Court Justice David Souter, who at times sits on the panel in Boston and who ruled in a similar case recently that a general participation in a conspiracy, even without a direct agreement, could constitute a bribe. However, the trial in that case had occurred before the ­Skilling decision was made.

DiMasi was sentenced to eight years in prison and ­McDonough to seven years following their convictions in 2011, in one of the highest-profile political corruption trials in recent memory.

A jury found that DiMasi used his power as speaker to help Cognos, a Burlington software company, win state contracts in exchange for payments to be made to his former law partner, payments that ultimately were directed to DiMasi.

McDonough, a lobbyist for Cognos, was convicted of helping to orchestrate the scheme. DiMasi and McDonough had argued that McDonough was simply doing his work as a lobbyist and that the payments to DiMasi’s legal partner could constitute a gift, but that there was never an agreement to accept a bribe to help Cognos win the contracts. A third man, Richard Vitale, DiMasi’s financial adviser, was acquitted.

A fourth man, Joseph P. ­Lally Jr., a Cognos salesman, pleaded guilty and testified about the scheme. He was sentenced to 18 months in prison.